PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Central potentials and canonical three-dimensional systems · Central potentials and canonical three-dimensional systems
The Structure of Quantum Mechanics, Ch Central potentials as a rotation problem
Problem
A finite spherical well of range a and depth V0 binds, among other states, exactly three states with l=1. Their reduced radial functions have 0, 1 and 2 nodes respectively for r>0; call these vP, vQ, vR.
((a)) Explain why the node theorem may be applied to order these three states even though it says nothing about comparing states of different l.
((b)) Order the energies EP, EQ, ER from lowest to highest.
((c)) The same well also binds an l=0 state whose u has one node. Does the node theorem say whether it lies above or below vP?